To solve problem (REF ), we adopt the FL algorithm in [1]}, which is summarized in Algorithm 1.
[t]
FL Algorithm
[1]
Initialize global regression vector \(w^0\)  and iteration number \(n=0\) .
Each user \(k\)  computes \(\nabla F_k(w^{(n)})\)  and sends it to the BS.
The BS computes \(\nabla F(w^{(n)})= \frac{1}{K}\sum _{k=1}^K \nabla F_k(w^{(n)})\) ,
which is broadcast to all users.
parallel for user \(k\in \mathcal {K}\) 
   Solve local FL problem (REF ) with a given learning accuracy \(\eta \)  and the solution is \(h_k^{(n)}\) .
   Each user sends \(h_k^{(n)}\)  to the BS.
end for
The BS computes \(w^{(n+1)}=w^{(n)}+\frac{1}{K} \sum _{k=1}^Kh_k^{(n)}\)  and broadcasts the value to all users.
Set \(n=n+1\) .
the accuracy \(\epsilon _0\)  of problem (REF ) is obtained.


In Algorithm 1, at each iteration of the FL algorithm, each user downloads the global FL model parameters from the BS for local computing, while the BS periodically gathers the local FL model parameters from all users and sends the updated global FL model parameters back to all users.
We define \(w^{(n)}\)  as the global FL parameter at a given iteration \(n\) .
Each user computes the local FL problem:
